cp's OEIS Frontend

A005664 Denominators of convergents to log_2 3.

%I A005664 M1428 #44 Jul 02 2025 16:01:54
%S A005664 1,1,2,5,12,41,53,306,665,15601,31867,79335,111202,190537,10590737,
%T A005664 10781274,53715833,171928773,225644606,397573379,6189245291,
%U A005664 6586818670,65470613321,137528045312,753110839881,5409303924479,6162414764360
%N A005664 Denominators of convergents to log_2 3.
%D A005664 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005664 T. D. Noe, <a href="/A005664/b005664.txt">Table of n, a(n) for n = 0..200</a>
%H A005664 Oliver K. Clay, <a href="https://doi.org/10.5642/jhummath.YQHO7207">The Long Search for Collatz Counterexamples</a>, J. Humanistic Math. (2023) Vol. 13, No. 2, 199-227. See p. 205.
%H A005664 R. E. Crandall, <a href="http://dx.doi.org/10.1090/S0025-5718-1978-0480321-3">On the 3x+1 problem</a>, Math. Comp., 32 (1978) 1281-1292.
%H A005664 E. G. Dunne, <a href="/DUNNE/TEMPERAMENT2.html">Pianos and Continued Fractions</a>
%H A005664 R. K. Guy, <a href="/A005663/a005663.pdf">Letter to N. J. A. Sloane, 1977</a>
%H A005664 David Ryan, <a href="http://arxiv.org/abs/1612.01860">An algorithm to assign musical prime commas to every prime number and construct a universal and compact free Just Intonation musical notation</a>, Preprint, arXiv preprint arXiv:1612.01860 [cs.SD], 2016.
%H A005664 Eric Weisstein's World of Music, <a href="http://www.ericweisstein.com/encyclopedias/music/CommaofPythagoras.html">Comma of Pythagoras</a>
%e A005664 log_2 3 = 1.5849625007211561814537389439...
%t A005664 Convergents[Log[2, 3], 30] // Denominator (* _Jean-François Alcover_, Dec 12 2016 *)
%o A005664 (PARI) a(n) = component(component(contfracpnqn(contfrac(log(3)/log(2), n)), 1), 2) \\ _Michel Marcus_, May 20 2013
%Y A005664 Cf. A005663, A028507, A020857.
%K A005664 nonn,frac,easy
%O A005664 0,3
%A A005664 _N. J. A. Sloane_, _R. K. Guy_
%E A005664 More terms from _James Sellers_, Sep 16 2000